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Parikh vectors
2RDG_1 3JTJ_1 1GTK_1 Letter Amino acid
11 17 27 R Arginine
9 10 10 Q Glutamine
2 6 6 M Methionine
12 19 19 I Isoleucine
19 7 8 K Lycine
6 7 3 F Phenylalanine
18 8 10 T Threonine
2 37 34 A Alanine
17 7 11 N Asparagine
16 15 19 D Aspartic acid
13 16 24 E Glutamic acid
0 3 4 C Cysteine
16 17 42 L Leucine
0 3 2 W Tryptophan
13 27 24 V Valine
9 8 5 Y Tyrosine
12 15 28 G Glycine
6 6 5 H Histidine
2 13 16 P Proline
13 12 16 S Serine 

2RDG_1|Chain A|Superantigen-like protein 11|Staphylococcus aureus (1280)
>3JTJ_1|Chain A|3-deoxy-manno-octulosonate cytidylyltransferase|Yersinia pestis (214092)
>1GTK_1|Chain A|PORPHOBILINOGEN DEAMINASE|ESCHERICHIA COLI (562)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
2RDG , Knot 89 196 0.80 36 138 191 
STLEVRSQATQDLSEYYNRPYFDLRNLSGYREGNTVTFINHYQQTDVKLEGKDKDKIKDGNNENLDVFVVREGSGRQADNNSIGGITKTNRTQHIDTVQNVNLLVSKSTGQHTTSVTSTNYSIYKEEISLKELDFKLRKHLIDKHDLYKTEPKDSKIRVTMKNGDFYTFELNKKLQTHRMGDVIDGRNIEKIEVNL
3JTJ , Knot 113 253 0.82 40 165 246 
SNAMSFIAIIPARYASTRLPGKPLADIAGKPMVVHVMERALASGADRVIVATDHPDVVKAVEAAGGEVCLTRADHQSGTERLAEVIEHYGFADDDIIVNVQGDEPLVPPVIIRQVADNLAACSAGMATLAVPIASSEEAFNPNAVKVVMDAQGYALYFSRATIPWERERFAQSKETIGDCFLRHIGIYAYRAGFIRRYVNWAPSQLEQIELLEQLRVLWYGEKIHVAVAKAVPAVGVDTQSDLDRVRAIMLNQ
1GTK , Knot 132 313 0.80 40 173 291 
MLDNVLRIATRQSPLALWQAHYVKDKLMASHPGLVVELVPMVTRGDVILDTPLAKVGGKGLFVKELEVALLENRADIAVHSMKDVPVEFPQGLGLVTICEREDPRDAFVSNNYDSLDALPAGSIVGTSSLRRQCQLAERRPDLIIRSLRGNVGTRLSKLDNGEYDAIILAVAGLKRLGLESRIRAALPPEISLPAVGQGAVGIECRLDDSRTRELLAALNHHETALRVTAERAMNTRLEGGCQVPIGSYAELIDGEIWLRALVGAPDGSQIIRGERRGAPQDAEQMGISLAEELLNNGAREILAEVYNGDAPA

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(2RDG_1)}(2) \setminus P_{f(3JTJ_1)}(2)|=84\), \(|P_{f(3JTJ_1)}(2) \setminus P_{f(2RDG_1)}(2)|=111\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:0010100010001000000101010010100010010110000000101010000010010000101111001010010000111100000000100100101110000100000100000010000101001010100011000010000100001010100101001010001000011011010010010101
Pair \(Z_2\) Length of longest common subsequence
2RDG_1,3JTJ_1 195 3
2RDG_1,1GTK_1 171 4
3JTJ_1,1GTK_1 150 4

Newick tree

 
[
	2RDG_1:96.62,
	[
		1GTK_1:75,3JTJ_1:75
	]:21.62
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{449 }{\log_{20} 449}-\frac{196}{\log_{20}196})=74.1\)
Status Protein1 Protein2 d d1/2
Query variables 2RDG_1 3JTJ_1 98 86.5
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]